Modeling reactive transport in sediments subject to bioturbation and compaction

Current bioturbation models are marked by confusion in their treatment of porosity. Different equations appear to be needed for different biodiffusion mechanisms, i.e., interphase mixing, where biological activity causes bulk mixing of sediment affecting both tracer and porosity profiles, versus intraphase mixing, where the solid components are intermixed, but the porosity is left unchanged. Another issue is whether the model depends upon the particle type with which tracers are associated, e.g., ¹³⁷Cs on small clay particles versus ²¹⁰Pb on larger grains. This uncertainty has lead to conflicting conservation equations for radiotracers, and in particular, to the question whether the porosity should be placed inside or outside of the differential term that governs the biodiffusive flux. We have reexamined this situation in the context of multiphase, multicomponent continuum theory. Most importantly, we prove that under the assumption of steady-state porosity, there exists only one correct form of the steady-state conservation equation for a radiotracer, regardless of biodiffusion mechanism and particle type, i.e.,